They need to pay that up front or within the normal pay period, end of the month or whatever. Short of pilferage from the company or other criminal type malfeasance with which they would have to charge you, what you have worked for and earned is yours with or without a signed termination agreement.
If they still insist, get it in writing and take what they have written and the termination agreement to the lawyer. Give them a reasonable time frame on when you will get back to them with an answer. You need not even mention lawyers. Just tell them you need it in writing to discuss with your financial adviser.
Yeah, it is definitely better to have it on your record that you quit rather than that you were terminated. But good employers also understand that there are jag-off employers who terminate for unjustified reasons.
I was the victim of a purely political termination some years ago. After 10 years or so, nobody even asks about it anymore. The first job I got after that one actually told me the straightforward manner in which I handled it was a reason I got hired. I won't go into the details on the reason for the termination, but it was basically because I refused to cooperate with the political lynching of my boss at the time because he was an honorable and decent man.
Good luck in your next position. I know this can be a major blow, particularly in an economy like this. But you can get through it with the help of family, friends and a good network. Let us know how you make out.
Funny you mention that. I've been on the "firing line" for doing the same thing. Although the 2 witches involved did get her fired. This happened a few years ago and they are still trying to get me fired.